论文标题
改善了某些谐波映射类别的BOHR不平等现象
Improved Bohr inequalities for certain classes of harmonic mappings
论文作者
论文摘要
$ f（z）= h+\ overline {g} $的谐波功能类别的BOHR半径在单位磁盘$ \ Mathbb {d}中：= \ {z \ in \ in \ mathbb {c}：| z | z | | <1 $ g（z）= \ sum_ {n = 1}^{\ infty} b_nz^n $是找到最大的半径$ r_f $，$ 0 <r_f <1 $ \ sum_ {n = 1}^{\ infty} \ left（| a_n |+|+| b_n | \ right）| z | |^n \ leq d（f（f（0），\ partial f（\ mathbb {d}}）） f（\ mathbb {d}））$是$ f（0）$和$ f（\ m athbb {d}）$之间的欧几里得距离。在本文中，我们证明了BOHR不平等的改进版本的两种型，一种用于某种类别的谐波和单价功能，另一种用于稳定的谐波映射。在论文中观察到，要获得尖锐的bohr不等式，就足以考虑数量$ s_r/π$的任何非负实际系数。由于主要结果，我们证明了推论，显示了尖锐的Bohr半径的精确值。
The Bohr radius for the class of harmonic functions of the form $ f(z)=h+\overline{g} $ in the unit disk $ \mathbb{D}:=\{z\in\mathbb{C} : |z|<1\} $, where $ h(z)=\sum_{n=0}^{\infty}a_nz^n $ and $ g(z)=\sum_{n=1}^{\infty}b_nz^n $ is to find the largest radius $ r_f $, $ 0<r_f<1 $ such that \begin{equation*} \sum_{n=1}^{\infty}\left(|a_n|+|b_n|\right)|z|^n\leq d(f(0),\partial f(\mathbb{D})) \end{equation*} holds for $ |z|=r\leq r_f $, where $ d(f(0),\partial f(\mathbb{D})) $ is the Euclidean distance between $ f(0) $ and the boundary of $ f(\mathbb{D}) $. In this paper, we prove two-type of improved versions of the Bohr inequalities, one for a certain class of harmonic and univalent functions and the other for stable harmonic mappings. It is observed in the paper that to obtain sharp Bohr inequalities it is enough to consider any non-negative real coefficients of the quantity $ S_r/π$. As a consequence of the main result, we prove corollaries showing the precise value of the sharp Bohr radius.
